ELK 503E - Power Electronic Systems

Course Objectives

The major objective of this graduate course is to introduce a variety of fundamental approaches to modeling the dynamics of power electronic circuits and their controllers.
Analytical approaches to modeling and understanding the dynamic behavior of power electronic systems will be presented and shown how to use these approaches in designing and evaluating practical feedback control systems. The emphasis will be on fundamental formulations that apply across a range of power electronic systems with illustrated extensive examples. The development of averaged models has also been considered beyond dc/dc converters, with generalizations to track the dynamics of the fundamental (and harmonics) converter waveforms. The analysis and feedback control of continuous-time (CT), linear, time-invariant (LTI) systems are described in the frequency domain and via LTI state-space models. The role of sampled data modeling and control in the stability evaluation of power electronic systems and its importance in the design of fully digital control systems will be retained. Simulations emphasizing the power electronic systems will also be covered.

Course Description

Students will have the fundamental knowledge of dynamic modeling and controlling power electronic systems.

Details of the Course Description:
Building the basis for analyzing the dynamic behavior of power circuits, and for designing and implementing controls that regulate the dynamics or errors, ensuring operation close to the desired condition, despite disturbances including variations and uncertainties in source, load, and circuit parameters, perturbations in switching times, startup and shutdown, or component failure. The focus will be on analysis and control design using appropriate models of dynamic behavior for both uncontrolled and controlled power converters.

Modeling approaches by introducing the idea of an averaged-circuit model will be discussed that is valuable in describing the behavior of dc/dc converters and other families of power circuits. The dynamics of the controller along with that of the power circuit will be modeled in order to study the controlled, closed-loop system. State-space models are introduced to embrace a much wider variety of modeling possibilities for converters and their controllers, which are also amenable to averaging. Circuit averaging will be applied to develop useful dynamic models for other categories of power converters, such as resonant converters, where the focus is on the local fundamental component. First, averaging is extended to broader classes of converters, including those for which the switch averaging is somewhat more subtle. Circuit averaging approaches for converters (such as resonant converters) in which the quantity of interest is not the local average value but rather the local fundamental. Later, state-space models for circuits and for more general systems (such as feedback controllers), and in both continuous time (CT) and discrete-time (DT) will be introduced.

The process of linearization for certain classes of nonlinear averaged-circuit models will be introduced. This will allow us to obtain LTI circuit models for small perturbations of averaged values from their constant values in nominal, steady-state operating conditions. These LTI models then serve as the basis for stability evaluation and control design of the power electronic converters.

The idea of circuit averaging is to derive an averaged model for the switch in high-frequency switched dc/dc converters and also obtain averaged-circuit models for the local component. The focus will be linearized the averaged switch, and illustrate the application of this linearized model to analyzing the small-signal behavior of the associated converters.

Modeling options will be extended to include state-space models. Both continuous-time signals, their averages, and their discrete-time samples in open- and closed-loop systems comprising power circuits and controllers. Linearized models given in state-space form will be used rather than the circuit form. Some key concepts and results for the analysis of LTI state-space models will be developed. Applications of these results to analyzing piecewise-LTI models and evaluating the stability of cyclic nominal operation in power circuits will be given.

The most typical route to usable LTI models in power electronics is the process of linearization, to describe small deviations around a constant steady. Such linearization will be illustrated using examples of average-circuit models. The design of feedback control to regulate a power converter in the vicinity of its nominal operating condition will be done on the basis of LTI models (usually obtained via linearization). The averaged-circuit models and the state-space models described in the course will be linearized around an operating point. The resulting LTI models can provide the basis for feedback control design. The application of the resulting linear models in stability evaluation and control design will be illustrated in the final stage of the course.

Computer simulations will be used as a part of the coursework.